Step 1 :The question is asking for the quotient of \(\frac{3}{5}\) divided by 6. To solve this, we need to divide \(\frac{3}{5}\) by 6. In terms of fractions, dividing by a number is the same as multiplying by its reciprocal. So, we need to multiply \(\frac{3}{5}\) by \(\frac{1}{6}\).
Step 2 :The result of the multiplication is \(\frac{3}{30}\). However, this fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
Step 3 :Final Answer: The quotient of \(\frac{3}{5} \div 6\) is \(\boxed{\frac{1}{10}}\). So, the correct option is a. \(\frac{1}{10}\).